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Simplifying (x + 3)(x + -1 + 4i)(x + -1 + -4i) = 0 Reorder the terms: (3 + x)(x + -1 + 4i)(x + -1 + -4i) = 0 Reorder the terms: (3 + x)(-1 + 4i + x)(x + -1 + -4i) = 0 Reorder the terms: (3 + x)(-1 + 4i + x)(-1 + -4i + x) = 0 Multiply (3 + x) * (-1 + 4i + x) (3(-1 + 4i + x) + x(-1 + 4i + x))(-1 + -4i + x) = 0 ((-1 * 3 + 4i * 3 + x * 3) + x(-1 + 4i + x))(-1 + -4i + x) = 0 ((-3 + 12i + 3x) + x(-1 + 4i + x))(-1 + -4i + x) = 0 (-3 + 12i + 3x + (-1 * x + 4i * x + x * x))(-1 + -4i + x) = 0 Reorder the terms: (-3 + 12i + 3x + (4ix + -1x + x2))(-1 + -4i + x) = 0 (-3 + 12i + 3x + (4ix + -1x + x2))(-1 + -4i + x) = 0 Reorder the terms: (-3 + 12i + 4ix + 3x + -1x + x2)(-1 + -4i + x) = 0 Combine like terms: 3x + -1x = 2x (-3 + 12i + 4ix + 2x + x2)(-1 + -4i + x) = 0 Multiply (-3 + 12i + 4ix + 2x + x2) * (-1 + -4i + x) (-3(-1 + -4i + x) + 12i * (-1 + -4i + x) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 ((-1 * -3 + -4i * -3 + x * -3) + 12i * (-1 + -4i + x) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 ((3 + 12i + -3x) + 12i * (-1 + -4i + x) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + (-1 * 12i + -4i * 12i + x * 12i) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 Reorder the terms: (3 + 12i + -3x + (-12i + 12ix + -48i2) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + (-12i + 12ix + -48i2) + 4ix * (-1 + -4i + x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + (-1 * 4ix + -4i * 4ix + x * 4ix) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 Reorder the terms: (3 + 12i + -3x + -12i + 12ix + -48i2 + (-4ix + 4ix2 + -16i2x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + (-4ix + 4ix2 + -16i2x) + 2x * (-1 + -4i + x) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + (-1 * 2x + -4i * 2x + x * 2x) + x2(-1 + -4i + x)) = 0 Reorder the terms: (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + (-8ix + -2x + 2x2) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + (-8ix + -2x + 2x2) + x2(-1 + -4i + x)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + -8ix + -2x + 2x2 + (-1 * x2 + -4i * x2 + x * x2)) = 0 Reorder the terms: (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + -8ix + -2x + 2x2 + (-4ix2 + -1x2 + x3)) = 0 (3 + 12i + -3x + -12i + 12ix + -48i2 + -4ix + 4ix2 + -16i2x + -8ix + -2x + 2x2 + (-4ix2 + -1x2 + x3)) = 0 Reorder the terms: (3 + 12i + -12i + 12ix + -4ix + -8ix + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: 12i + -12i = 0 (3 + 0 + 12ix + -4ix + -8ix + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + 12ix + -4ix + -8ix + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: 12ix + -4ix = 8ix (3 + 8ix + -8ix + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: 8ix + -8ix = 0 (3 + 0 + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + 4ix2 + -4ix2 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: 4ix2 + -4ix2 = 0 (3 + 0 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 (3 + -48i2 + -16i2x + -3x + -2x + 2x2 + -1x2 + x3) = 0 Combine like terms: -3x + -2x = -5x (3 + -48i2 + -16i2x + -5x + 2x2 + -1x2 + x3) = 0 Combine like terms: 2x2 + -1x2 = 1x2 (3 + -48i2 + -16i2x + -5x + 1x2 + x3) = 0 Solving 3 + -48i2 + -16i2x + -5x + 1x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -48i2 + -16i2x + -5x + 1x2 + -3 + x3 = 0 + -3 Reorder the terms: 3 + -3 + -48i2 + -16i2x + -5x + 1x2 + x3 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -48i2 + -16i2x + -5x + 1x2 + x3 = 0 + -3 -48i2 + -16i2x + -5x + 1x2 + x3 = 0 + -3 Combine like terms: 0 + -3 = -3 -48i2 + -16i2x + -5x + 1x2 + x3 = -3 Add '5x' to each side of the equation. -48i2 + -16i2x + -5x + 1x2 + 5x + x3 = -3 + 5x Reorder the terms: -48i2 + -16i2x + -5x + 5x + 1x2 + x3 = -3 + 5x Combine like terms: -5x + 5x = 0 -48i2 + -16i2x + 0 + 1x2 + x3 = -3 + 5x -48i2 + -16i2x + 1x2 + x3 = -3 + 5x Add '-1x2' to each side of the equation. -48i2 + -16i2x + 1x2 + -1x2 + x3 = -3 + 5x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -48i2 + -16i2x + 0 + x3 = -3 + 5x + -1x2 -48i2 + -16i2x + x3 = -3 + 5x + -1x2 Add '-1x3' to each side of the equation. -48i2 + -16i2x + x3 + -1x3 = -3 + 5x + -1x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -48i2 + -16i2x + 0 = -3 + 5x + -1x2 + -1x3 -48i2 + -16i2x = -3 + 5x + -1x2 + -1x3 Reorder the terms: 3 + -48i2 + -16i2x + -5x + x2 + x3 = -3 + 5x + -1x2 + -1x3 + 3 + -5x + x2 + x3 Reorder the terms: 3 + -48i2 + -16i2x + -5x + x2 + x3 = -3 + 3 + 5x + -5x + -1x2 + x2 + -1x3 + x3 Combine like terms: -3 + 3 = 0 3 + -48i2 + -16i2x + -5x + x2 + x3 = 0 + 5x + -5x + -1x2 + x2 + -1x3 + x3 3 + -48i2 + -16i2x + -5x + x2 + x3 = 5x + -5x + -1x2 + x2 + -1x3 + x3 Combine like terms: 5x + -5x = 0 3 + -48i2 + -16i2x + -5x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 3 + -48i2 + -16i2x + -5x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 3 + -48i2 + -16i2x + -5x + x2 + x3 = 0 + -1x3 + x3 3 + -48i2 + -16i2x + -5x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3 + -48i2 + -16i2x + -5x + x2 + x3 = 0 The solution to this equation could not be determined.
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